Research Of NPML Absorption Boundary Conditions And Periodic Boundary Conditions Based On FCC-FDTD Algorithm

Since Maxwell established the fundamental equation of electromagnetic field,many scholars have made a lot of achievements in the field of electromagnetic wave.With the third industrial revolution,Computational Electromagnetics with computer as the carrier has obtained great development.In 1966,Yee proposed the Finite-Difference Time-Domain(FDTD)method for the first Time in the world.The method is simple to implement and easy to understand.In the following decades,it has become a hot research object,and the related results emerge one after another,and it has been continuously improved.Based on Maxwell's equation,the FDTD method samples the electric field and magnetic field alternately,but the distribution of the field quantity is sparse,so there is always a lack of precision,which is easy to cause anisotropy.In order to improve this problem,many scholars put forward many solutions.In recent years,a new kind of grid was proposed--Face Center Cube Mesh(FCC grid).Different from the FDTD method with Yee cell,the FCC-FDTD method has a large distribution density of the field.Therefore,the FCC-FDTD method has a good isotropic effect and higher precision,especially in the two-dimensional and three-dimensional problems.In this thesis,based on the previous work,the absorption boundary conditions of NPML and periodic boundary conditions based on FCC grid are studied and verified by examples.Firstly,the characteristics of FCC grid were introduced in detail in this thesis,and the relationship between electric field and magnetic field in the FCC grid were presented,too.Then the iterative formula of FCC-FDTD method is briefly introduced.Secondly,this thesis focuses on the absorption boundary of Nearly Perfectly Matched Layer(NPML)based on FCC grid.The principle of NPML method is introduced and the absorption boundary of FCC-FDTD method is derived.Then the iterative formula are given.The simulation results are compared with UPML of the traditional FDTD,and the correctness is verified.The results show that the NPML absorption boundary has a good absorption effect.Finally,the periodic boundary conditions(PBC)are studied based on FCC grid.Based on Floquet theorem,the iterative formula of periodic boundary conditions are derived in detail based on the FCC-FDTD method under the vertical incidence conditions.The correctness of the periodic boundary condition is proved by an example of the electromagnetic scattering of an infinite medium plate.At the same time,that the NPML absorption boundary and PBC based on FCC-FDTD method are proved by this example.